Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 50000)	Who ?	When ?
8001	(4^111231+23)/3	66968	Robert Price	02/2017
8002	16206^13549+13549^16206	66962	Hans Havermann	08/2019
8003	2^222408-111275	66952	Enzo Doria	05/2014
8004	10^66949-9^66949	66949	Jean-Louis Charton	12/2005
8005	2^222378-1005	66943	Lelio R Paula	04/2012
8006	(9*2^222366+1)/73	66938	Lelio R Paula	08/2012
8007	7^79202-6^(79202+1)	66934	Robert Price	06/2016
8008	2^222325-112255	66927	Enzo Doria	06/2014
8009	21789^1178+1178^21789	66918	Hans Havermann	08/2019
8010	20^51428+33	66910	Lelio R Paula	08/2013
8011	2^222224-18509	66897	Enzo Doria	05/2013
8012	(38*10^66896+187)/9	66897	Robert Price	11/2017
8013	2^222192-869688105	66887	Lelio R Paula	02/2016
8014	(19*10^66878-43)/3	66879	Robert Price	10/2017
8015	11^64219-64	66878	Lelio R Paula	07/2013
8016	2^222151-17295	66875	Lelio R Paula	04/2012
8017	gcd(V(799885),5F(159977)(F(159977)+1)+1)	66867	Serge Batalov	04/2015
8018	2^222085-111031	66855	Enzo Doria	05/2014
8019	8*10^66848-13	66849	Robert Price	05/2017
8020	(3^140087+4)/13	66838	Lelio R Paula	04/2012
8021	(3^140102+4)/8843609437	66836	Lelio R Paula	04/2012
8022	19^52265+52	66835	Lelio R Paula	08/2013
8023	2*10^66826-27	66827	Robert Price	02/2017
8024	4*6^85867+5	66819	Lelio R Paula	09/2014
8025	11955^16384+2	66807	Matt Stath	12/2018
8026	15^56800+8	66802	Lelio R Paula	08/2013
8027	(2^221891-2^110946+1)/5	66796		11/2006
8028	10^66793+69441	66794	Patrick De Geest	05/2013
8029	10^66793-63	66793	Robert Price	05/2011
8030	35^43256-1704	66791	Enzo Doria	03/2013
8031	3^139976+2^(139976-1)	66786	Robert Price	05/2016
8032	88769!6-48	66786	Robert Price	08/2018
8033	7^79023-54	66783	Lelio R Paula	06/2013
8034	104^33109-103	66782	Norbert Schneider	11/2016
8035	(34*10^66778-7)/9/37/358901	66772	Makoto Morimoto	04/2016
8036	(-lucasV(1,2,443622)+2)/(7281487)	66766	Mike Oakes	04/2017
8038	2^221768+183	66759	Lelio R Paula	02/2012
8037	gcd(V(1197915),5F(239583)(F(239583)+1)+1)	66759	Serge Batalov	04/2015
8039	(154*10^66755-1)/9	66757	Serge Batalov	12/2014
8040	11^64097+48	66751	Lelio R Paula	07/2013
8041	(lucasV(1,2,443547)-2)/(713791327221773)	66749	Mike Oakes	04/2017
8042	(19*10^66748+413)/9	66749	Robert Price	10/2017
8043	(3*2^221696-1)/13	66737	Lelio R Paula	01/2014
8044	8*6^85758-7	66734	Lelio R Paula	09/2014
8045	135^31325+2	66733	Lelio R Paula	05/2013
8046	(49*10^66729+41)/9	66730	Robert Price	07/2015
8047	(349*10^66720-7)/9	66722	Robert Price	03/2017
8048	(-lucasV(1,2,443285)+2)/(3^2*307)	66718	Mike Oakes	04/2017
8049	(25*10^66714+71)/3	66715	Robert Price	01/2017
8050	11^64061-780	66713	Enzo Doria	11/2012
8051	7^78929+4	66703	Lelio R Paula	06/2013
8052	11^64048-930	66700	Enzo Doria	11/2012
8053	120^32079-119	66699	Norbert Schneider	09/2018
8054	2*7^78921+5	66697	Lelio R Paula	09/2014
8055	(25*2^221526+1)/409	66685	Lelio R Paula	08/2012
8056	16330^12117+12117^16330	66682	Hans Havermann	08/2019
8057	(2^221509-1)/292391881	66673	Jens K. Andersen	02/2009
8058	2^221479+72953	66672	Enzo Doria	04/2016
8060	10^66666+275403	66667	Patrick De Geest	03/2010
8059	16317^12182+12182^16317	66667	Hans Havermann	08/2019
8061	10^66666-115521	66666	Patrick De Geest	03/2010
8062	(18*10^66657-81)/99	66657	Ray Chandler	01/2011
8063	4*10^66653+21	66654	Robert Price	08/2016
8064	(10^66650+149)/3	66650	Serge Batalov	12/2014
8065	9^69842+38^69842-24^69842-3*2^69842	66647	Mike Oakes	12/2010
8066	2^221391-2145	66646	Lelio R Paula	04/2012
8067	22952^801+801^22952	66645	Hans Havermann	08/2019
8068	(5*10^66613-119)/3	66614	Robert Price	04/2016
8069	2^221273-113233	66610	Enzo Doria	07/2014
8070	3^139571-46	66593	Lelio R Paula	06/2013
8071	(410^(233295)-2*(10^33295)+1)/3	66591	Robert Price	04/2018
8072	2^221181-869688105	66583	Lelio R Paula	02/2016
8073	(61*10^66575-7)/9	66576	Ray Chandler	02/2012
8074	2^221126+133	66566	Lelio R Paula	02/2012
8075	12^61680+91	66564	Lelio R Paula	07/2013
8076	(lucasV(1,2,442258)+2)/103	66564	Mike Oakes	04/2017
8077	(13*10^66551-73)/3	66552	Robert Price	12/2016
8078	11^63901-1590	66547	Enzo Doria	12/2012
8079	11^63901-1500	66547	Enzo Doria	12/2012
8080	6^85517+23	66546	Lelio R Paula	07/2013
8081	17^54069-40	66530	Lelio R Paula	08/2013
8082	(2^110503+4725)^2+(2^110503+4725)+41	66530	Makoto Morimoto	05/2016
8083	(2^110503+8099)^2+(2^110503+8099)+41	66530	Makoto Morimoto	05/2016
8085	(2^221008-1017)/78533	66526	Lelio R Paula	04/2012
8084	3^139432+26	66526	Lelio R Paula	06/2013
8086	((2^110503+5139)^2+(2^110503+5139)+41)/20865797	66523	Makoto Morimoto	05/2016
8087	((2^110503+6647)^2+(2^110503+6647)+41)/197/17327	66523	Makoto Morimoto	05/2016
8088	6^85481+85481	66518	Henri Lifchitz	08/2014
8089	(9179*2^220913-1)/399	66503	Lelio R Paula	04/2015
8090	13^59687+66	66488	Lelio R Paula	07/2013
8091	(49*10^66485-31)/9	66486	Robert Price	07/2015
8092	(46*10^66469+17)/9	66470	Robert Price	06/2015
8093	2^220790+97	66465	Lelio R Paula	02/2012
8094	(23*2^220790+1)/807	66463	Lelio R Paula	06/2012
8095	40009^14441-102	66460	Enzo Doria	07/2012
8096	2^220736-143	66449	Lelio R Paula	02/2012
8097	61077!4-64	66448	Robert Price	11/2019
8098	(79*10^66447-97)/99	66447	Ray Chandler	01/2011
8099	21235^1344+1344^21235	66432	Hans Havermann	08/2019
8100	2^220675+69	66430	Lelio R Paula	02/2012
8101	19049^3070+3070^19049	66427	Hans Havermann	08/2019
8102	88323!6-16	66419	Robert Price	08/2018
8103	2^220633-111381	66418	Enzo Doria	05/2014
8104	(2^220625-509203)/4000321	66409	Lelio R Paula	05/2012
8105	2^220596-15813	66407	Enzo Doria	04/2013
8106	(5*10^66394-17)/3	66395	Serge Batalov	05/2009
8107	2^220549-1859173	66392	Enzo Doria	04/2016
8108	2^220478-161	66371	Lelio R Paula	02/2012
8109	5^94938-14636	66359	Enzo Doria	02/2013
8110	(F(67)^4861-F(66)^4861)/F(65)	66353	Wayne Halsdorf	03/2012
8111	15444^15839-15839^15444	66346	Norbert Schneider	08/2018
8112	2^220253-114871	66303	Enzo Doria	05/2015
8113	12^61432+95	66297	Lelio R Paula	07/2013
8114	2^220192-111563	66285	Enzo Doria	05/2014
8115	2^220188-111449	66284	Enzo Doria	05/2014
8116	(4*10^66284+23)/9	66284	Robert Price	11/2014
8117	32501!2+2	66266	Robert Price	01/2015
8118	(8*10^66261-101)/3	66262	Robert Price	10/2017
8119	1530*10^66254+R(66254)	66258	Patrick De Geest	05/2016
8120	(47^39623-1)/46	66252	Robert Price	06/2014
8121	2^220044-97305	66240	Lelio R Paula	04/2012
8122	(77*10^66237-257)/9	66238	Robert Price	10/2017
8123	29^45285+2	66225	Ray Chandler	08/2011
8124	16711^9178+9178^16711	66222	Hans Havermann	08/2019
8125	15^56289+38	66202	Lelio R Paula	08/2013
8126	3^138749+98	66201	Lelio R Paula	06/2013
8127	(21*2^219912-1)/5	66201	Lelio R Paula	01/2014
8129	2^219904-16995	66198	Lelio R Paula	10/2011
8128	2^219903-4615	66198	Yves Minet	05/2019
8130	(3^138712-2)/5297	66179	Lelio R Paula	04/2012
8131	Phi(198552,10)	66177	Ray Chandler	07/2010
8132	4*6^85041+7	66176	Lelio R Paula	09/2014
8133	16777^8794+8794^16777	66172	Hans Havermann	08/2019
8134	2^219812-3149	66171	Yves Minet	10/2009
8135	2^219795-611167	66165	Paul Bourdelais	03/2013
8136	32455!2+512	66162	Robert Price	02/2015
8137	(27*2^219760-1)/227	66154	Lelio R Paula	01/2014
8139	(11^63521-4^63521)/7	66150	Robert Price	03/2013
8138	5*7^78274-6	66150	Lelio R Paula	09/2014
8140	15853^14872+14872^15853	66145	Hans Havermann	08/2019
8141	(-lucasV(1,2,439441)-2)/(31192781359)	66134	Mike Oakes	04/2017
8142	2^219679-112015	66130	Enzo Doria	05/2014
8143	2^219653+15015*219653	66123	Henri Lifchitz	04/2005
8144	15445^15782-15782^15445	66108	Norbert Schneider	08/2018
8145	2^219600+76561	66107	Enzo Doria	05/2016
8146	2^219594+255255	66105	Lelio R Paula	10/2011
8147	4*7^78210-3	66096	Lelio R Paula	09/2014
8148	(15185*2^219557-1)/63	66096	Lelio R Paula	04/2015
8149	(19*2^219499-1)/13	66076	Lelio R Paula	01/2014
8150	2^219496+66615	66075	Lelio R Paula	10/2011
8151	(F(79021)^5-F(79020)^5)/F(79019)	66057	Wayne Halsdorf	03/2012
8152	15871^14500+14500^15871	66046	Hans Havermann	08/2019
8154	(2^219414+7)/443657	66045	Lelio R Paula	04/2012
8153	(115*10^66043-1)/3	66045	Serge Batalov	12/2014
8155	10^66033+19	66034	Robert Price	01/2011
8156	10^66033-78309	66033	Patrick De Geest	05/2013
8157	(lucasV(1,2,438701)+2)/7599419	66025	Mike Oakes	04/2017
8158	2^219304+454245	66018	Henri Lifchitz	03/2007
8159	(27*2^219293+1)/9145	66012	Lelio R Paula	08/2012
8160	2^219273-112635	66008	Enzo Doria	06/2014
8161	17548^5771+5771^17548	66003	Hans Havermann	08/2019
8162	2^219250+25	66001	Lelio R Paula	08/2011
8163	132^31123+131	65999	Norbert Schneider	03/2015
8164	19327^2598+2598^19327	65995	Hans Havermann	08/2019
8165	18440^3789+3789^18440	65988	Hans Havermann	08/2019
8166	V(319871)	65987	Serge Batalov	03/2015
8167	2^219189-195	65983	Lelio R Paula	08/2011
8168	(7*2^219143-1)/55	65968	Lelio R Paula	01/2014
8169	(73^35401-1)/72	65962	Paul Bourdelais	08/2017
8170	2^219112-17009	65960	Enzo Doria	05/2013
8171	2^219093-111201	65954	Enzo Doria	05/2014
8172	2^219089-112099	65953	Enzo Doria	06/2014
8173	46714!3+81	65950	Robert Price	09/2014
8174	(11*10^65944-131)/3	65945	Robert Price	02/2017
8175	2^219021-3553	65932	Yves Minet	03/2017
8176	Pell-LucasQ(172243)/2	65931	Eric W. Weisstein	01/2007
8177	2^218990+73519	65923	Enzo Doria	04/2016
8178	58^37378-57	65914	Norbert Schneider	09/2014
8180	(2^218945-7)/1675	65906	Lelio R Paula	04/2012
8179	5*10^65905+81	65906	Robert Price	08/2017
8181	3*10^65899-13	65900	Robert Price	11/2017
8182	(-lucasV(1,2,437845)-2)/1679917	65896	Mike Oakes	04/2017
8183	127^31322-2	65896	Lelio R Paula	10/2017
8184	2^218897-111889	65895	Enzo Doria	05/2014
8185	2^218896+1869451	65895	Enzo Doria	05/2016
8186	63^36616+2	65885	Lelio R Paula	05/2013
8187	(3*2^218822-1)/11	65872	Lelio R Paula	01/2014
8188	2^218796-113297	65865	Enzo Doria	07/2014
8189	2^218797+73727	65865	Enzo Doria	04/2016
8190	3^138040-110	65862	Lelio R Paula	06/2013
8191	11^63240-1950	65858	Enzo Doria	12/2012
8192	2^218764-111873	65855	Enzo Doria	05/2014
8193	(34*10^65839-7)/9/37	65839	Makoto Morimoto	04/2016
8194	3^137988+26	65838	Lelio R Paula	06/2013
8195	2^218680-719	65830	Yves Minet	05/2012
8196	18^52424+17	65807	Lelio R Paula	08/2013
8197	19062^2827+2827^19062	65790	Hans Havermann	08/2019
8198	(2*15683^15683+1)/732384425	65789	David Broadhurst	09/2010
8199	(23*2^218517+1)/19003	65778	Lelio R Paula	07/2012
8200	(5*10^65773+1)/3	65774	Erik Branger	12/2013
8201	160^29839-159	65769	Norbert Schneider	12/2018
8202	2^218457-17329	65763	Enzo Doria	05/2013
8203	151703#+223381	65759	Nicolas PALAU	10/2016
8204	2^218436+40755	65756	Lelio R Paula	10/2011
8205	2^218399-4627	65745	Yves Minet	05/2019
8206	(F(44)^7433-F(43)^7433)/F(42)	65744	Wayne Halsdorf	03/2012
8207	15952^13219+13219^15952	65742	Hans Havermann	08/2019
8208	157^29934+29934^157	65733	Serge Batalov	05/2014
8209	211^28273-2	65715	Lelio R Paula	09/2013
8210	(59*10^65712+31)/9	65713	Robert Price	09/2015
8211	611^23586+23586^611	65712	Norbert Schneider	08/2016
8212	p(13991)#/2+32	65712	Robert Price	12/2016
8213	15865^13864+13864^15865	65712	Hans Havermann	07/2019
8214	2^218282-18485	65710	Enzo Doria	05/2013
8215	2^218274-111251	65708	Enzo Doria	05/2014
8216	2*F(314335)-1	65693	Henri Lifchitz	12/2009
8217	2^218200+427	65685	Henri Lifchitz	01/2005
8218	(10199^16384+10197^16384)/2	65676	Jeppe Stig Nielsen	04/2018
8219	(10199^(2^14)+(10197)^(2^14))/2	65676	Robert Price	05/2018
8220	46532!3+3	65667	Robert Price	10/2014
8221	2^218120-147	65661	Lelio R Paula	08/2011
8222	452^24729+24729^452	65659	Norbert Schneider	09/2016
8223	5817^17440+17440^5817	65657	Norbert Schneider	06/2019
8224	2^218102-114893	65656	Enzo Doria	05/2015
8225	(15*2^218083-1)/17	65650	Lelio R Paula	01/2014
8226	(15*2^218081+1)/18941	65646	Lelio R Paula	08/2012
8227	15818^14115+14115^15818	65640	Hans Havermann	08/2019
8228	(306^26407-1)/305	65638	Eric Chen	09/2017
8230	19^51326+36	65634	Lelio R Paula	08/2013
8229	(21*2^218045-1)/451583	65634	Lelio R Paula	01/2014
8231	2^217989-33	65622	Lelio R Paula	08/2011
8232	(13*2^217961+1)/3	65614	Lelio R Paula	06/2012
8233	4*6^84315-5	65611	Lelio R Paula	09/2014
8234	(315047^11933+1)/315048	65607	Faysal YAtim	06/2008
8235	6^84303+55	65601	Lelio R Paula	07/2013
8236	16585^9024+9024^16585	65601	Hans Havermann	08/2019
8237	18462^3575+3575^18462	65601	Hans Havermann	08/2019
8238	15963^12862+12862^15963	65597	Hans Havermann	08/2019
8239	(-lucasV(1,2,435857)+2)/(1738598017)	65595	Mike Oakes	04/2017
8240	(9787*2^217873-1)/37	65589	Lelio R Paula	04/2015
8241	5*2^217858+3	65583	Lelio R Paula	04/2014
8242	(19*10^65572+119)/3	65573	Robert Price	02/2017
8244	20^50399+51	65571	Lelio R Paula	08/2013
8243	7162^17009+17009^7162	65571	Norbert Schneider	07/2018
8245	11^62946-5670	65552	Enzo Doria	01/2013
8246	2^217742-3911	65547	Yves Minet	08/2009
8247	(19*10^65545+77)/3	65546	Robert Price	08/2016
8248	2^217731+131	65544	Lelio R Paula	08/2011
8249	2^217720-111287	65541	Enzo Doria	05/2014
8250	(365^25579+1)/366	65539	Eric Chen	10/2017

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Probable Primes Top 10000

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